The high resolution optical measurement of rotation is usually made by means of a radial diffraction grating of micron scale or submicron scale period in the form of a ring defined at the surface of a rotating encoder disk as shown in document U.S. Pat. No. 5,498,870. The two diffraction orders diffracted in transmission or in reflection, directed along and opposite to the tangential displacement direction at the impact point of an incident beam experience an optical phase shift of opposite sign proportional to the local linear displacement and are recombined by means of a second, non-rotating, radial grating which directs both phase shifted diffracted beams in a common direction where they interfere. For the interference contrast to be close to one (1), the relative positioning of the two radial gratings must be precise and stable during relative rotation. The smaller the encoder disk, the more critical the relative positioning conditions between the disk grating and the second grating. A small grating ring diameter implies in particular that the length of the radial grating lines must be short if an acceptable contrast is to be preserved upon relative rotation in the presence of eccentricity due to imperfect alignment between the rotation axis and the center of the encoder disk, and due to mechanical shocks; this in turn implies that the fraction of optical power impinging onto the encoder disk and experiencing diffraction and interference decreases with a decrease of the encoder disk diameter in order to preserve an acceptable interference contrast as described in document Yves Jourlin, Olivier Parriaux, and Jörg Fuchs, “Miniature holistic displacement sensor by immersion diffractive interferometry,” Opt. Express 17, 9080-9088 (2009). As a result, a rotation encoder of small diameter of the state of the art either has its interference contrast spoiled by the least eccentricity or uses only a very small fraction of the available power of the light source.
It is therefore desirable to adopt a diffractive interferometric scheme which is little sensitive to eccentricity and in which most of the power delivered by the light source participates in the interference between the orders carrying the information on the rotation. This can be achieved by using two cylindrical gratings where the grating lines are parallel to the rotation axis and are defined on the circularly cylindrical wall of a circular encoder disk or rod.
It is to be noted that cylindrical gratings would not only be useful for stand alone rotation sensors. They could be used in direct drive systems where there is no room to place a standalone rotation encoder; therefore the encoding grating must be defined at the wall of the shaft. Beyond rotation measurement applications, there are other applications in metrology, in spectroscopy, and more generally in diffractive optics involving cylindrical waves, where fine pitch cylindrical gratings are needed.
The main difficulty in defining a possibly submicron short period corrugation grating at the wall of a circular plate or circular rod is to print an integer number of parallel grating lines and grooves in a closed circle without stitching error, and to print this cylindrical grating with strictly constant period, i.e., without wobble in the spatial frequency. The solution consisting in wrapping and pasting a thin plane grating of rectilinear lines around a cylindrical surface as disclosed in document JP 7146405 does not permit a precise stitching between the last and the first grating lines. Usually, the encoder disk is placed on a high accuracy lathe; a tool machines or prints the grating lines parallel to the rotation axis every increment of the angular abscissa as disclosed in document WO 99/20427 “Method for manufacturing of optical torque transducer”. The regularity of the period and the accuracy of the stitching is however limited which makes such approach improper for fine pitch cylindrical gratings. It is therefore desirable to have a grating printing method which permits to solve the above mentioned problems.
It is to be noted that the LIGA process permits transferring the pattern of a thick planar metal mask into a polymer substrate by means of an almost diffraction-less X-ray beam. However, if the pattern of the X-ray mask is the corrugated edge of a metal layer defining a crenellation of micrometer or submicrometer period and submicrometer depth, the imperfect collimation of the X-ray beam results in a smoothing out of the corrugation on the wall at less than 1 millimeter under the metal mask as illustrated in document by C. J. Moran-Iglesias, A. Last, J. Mohr, “Improved grating spectrometer”, Prod. SPIE, Vol. 5962, pp. 596225.1-596225.9. The LIGA process is thus not efficient for fabricating uniform cylindrical corrugations having long lines. This is a great limitation.